On the other hand, from the numerical point of view, the tangential velocity redistributes the points on the curve (see [1]}, [2]}, [3]}, [4]}): this improves both the stability and the robustness of numerical computations. To redistribute the points asymptotically uniformly, we enrich the model as follows
\(\frac{\partial \textbf {x}}{\partial t}=\beta \textbf {N}+\alpha \textbf {T},\) 
